Select the correct answer from each drop-down menu.
A deli owner has determined that his revenue, y, from selling sandwiches each day is at most
, where x represents the number of sandwiches he sells. To make a profit, his revenue must be greater than his costs, represented by the expression
.
Write a system of inequalities to represent the values of x and y where the deli owner makes a profit. Then complete the statements.
The point (30,90) is ________ of this system
A. a viable solution
B. not a solution
C. both a viable and nonviable solution
D. a nonviable solution
The point (60,160) is ________ of this system.
A. a viable solution
B. not a solution
C. both a viable and nonviable solution
D. a nonviable solution
To represent the values of x and y where the deli owner makes a profit, we can set up the following system of inequalities:
y ≤ 30x
y > 20x + 100
The point (30,90) satisfies both inequalities since 90 ≤ 30(30) and 90 > 20(30) + 100. Therefore, it is a viable solution.
The point (60,160) also satisfies both inequalities since 160 ≤ 30(60) and 160 > 20(60) + 100. Therefore, it is also a viable solution.
Therefore, the correct answers are:
The point (30,90) is a viable solution.
The point (60,160) is a viable solution.